English

Fractional integration for irregular martingales

Probability 2020-09-14 v1 Classical Analysis and ODEs

Abstract

We suggest two versions of the Hardy--Littlewood--Sobolev inequality for discrete time martingales. In one version, the fractional integration operator is a martingale transform, however, it may vanish if the filtration is excessively irregular; the second version lacks the martingale property while being analytically meaningful for an arbitrary filtration.

Keywords

Cite

@article{arxiv.2009.05293,
  title  = {Fractional integration for irregular martingales},
  author = {Dmitriy Stolyarov and Dmitry Yarcev},
  journal= {arXiv preprint arXiv:2009.05293},
  year   = {2020}
}

Comments

8 pages

R2 v1 2026-06-23T18:28:00.786Z